Finite Group Databasebeta

C22×#11763782 #17979442

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#11763782

Splittings

SylowC17 ⋊ C22×#408

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC23×D4×C17C4
socleC24×C17C22×C4
prime radicalC23×#63254C2
cosocleC2×Dic17C25
hypercenterC23×D4#595
hypocenterC17C22×#408
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×D4

5326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

272 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114686);